Triple points and triple lines for pure substances and mixtures
My understanding is that pure substances can have triple points. But mixtures of substances have triple lines, i.e. there isn't a single point but a one-dimensional path in $PT$ space where three phases can coexist.
This is understanding comes from the Gibbs phase rule that $F = C - P + 2$, where $F$ is the degrees of freedom, $C$ is the number of components, and $P$ is the number of phases. At a triple point (or triple line) $P = 3$. For a two-component system like a mixture of ethanol and water, $C = 2$. If we apply the equation, then we find that in this case, $F = 1$, i.e. there is one degree of freedom. If we pick $P$ then $T$ is defined for us by the constraints of any two-component, three-phase system. That's a "triple line". For a one-component system, the equation says that if $C = 1$ and $P = 3$, then $F = 0$. A triple point. We don't get to pick either $P$ or $T$.
Water isn't exactly a pure substance
But, ordinary water is not actually a pure substance. It is a mixture of different isotopologues, e.g. $\ce{HDO}$ and $\ce{H2^{18}O}$, etc. It is also a mixture of para- and ortho-isomers that differ only in the relative spin states of the two $\ce{H}$ atoms, as I learned from reading this very site the other day.
Does ordinary water have a triple point?
Pure $\ce{D2O}$ has a triple point distinct from that of $\ce{H2O}$. For example, one web site says that $\ce{H2O}$ has a triple point of 612 Pa and 0.01 °C, while $\ce{D2O}$ reportedly has a triple point of 661 Pa and 3.82 °C. But most (all?) water samples in the world are not 100% isotopically pure. And very little work has been done separating para- and ortho spin isomers of water.
So given that water isn't a pure substance, how does it have a well-defined triple point? "The" triple point of water was until recently fixed by the definition of SI units, so it seems that for most practical purposes the impurities in water don't matter much. Why not? What is the triple point of para-$\ce{H2O}$? Of ortho-$\ce{H2O}$? Of para-$\ce{H2^{18}O}$? Etc. etc. etc. Why doesn't the phase rule apply to these species?